# Research

My most-recent preprint is co-authored with Ewan Davies, Alex Karduna, and Holden Lee. We prove rapid mixing of Glauber dynamics (a Markov chain) on the collection of list packings of a graph. The preprint is available here.

A recent preprint is co-authored with Alain Oliviero Durmus, Pierre Monmarche, and Gabriel Stoltz. We prove explicit nonasymptotic convergence rates of generalized Hamiltonian Monte Carlo (an MCMC method). The preprint is available here.

My dissertation studied the existence-and-convergence-to equilibrium for the degenerate stochastic Lorenz 96 model, a finite-dimensional ODE analogue to the Navier-Stokes equations. The manuscript is available here.

My postdoctoral appointment is co-advised by Olivier Pinaud and David Aristoff. We are currently investigating stochastic homogenization for media with antisymmetric matrix fields.

## An example of Langevin dynamics

## A recent research presentation

# Research with Undergraduates

I was privileged enough to participate in mathematics research as an undergraduate at Concordia College, as well as through an NSF-funded research program at New York University. These experiences were invaluable to my future career as a mathematician, and I try to participate in leading undergraduate research whenever possible. The list of program topics I have led with undergraduates includes:

Smoothing of Markov semigroups

Fractals and iterated function systems

Sampling and interpolation theory

Markov chains and mixing times

Models for turbulent flow

Semigroup theory

Fractional operator theory

Selected Publications:

Second order quantitative bounds for unadjusted generalized Hamiltonian Monte Carlo

Weighted L2-contractivity of Langevin dynamics with singular potentials

Sampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1]

Stability of the Kaczmarz reconstruction for stationary sequences

A tractable numerical model for exploring nonadiabatic quantum dynamics

Links to my research profiles: